Generic stability of the spectra for bounded linear operators on Banach spaces.
Generic well-posedness for a class of equilibrium problems.
Geometric characteristic of semi-Fredholm operators and their asymptotic behaviour
Geometric characteristics for convergence and asymptotics of successive approximations of equations with smooth operators
We discuss the problem of characterizing the possible asymptotic behaviour of the iterates of a sufficiently smooth nonlinear operator acting in a Banach space in small neighbourhoods of a fixed point. It turns out that under natural conditions, for the most part of initial approximations these iterates tend to "lie down" along a finite-dimensional subspace generated by the leading (peripherical) eigensubspaces of the Fréchet derivative at the fixed point and moreover the asymptotic behaviour of...
Geometric proofs of composition theorems for generalized Fourier integral operators.
Geometric properties of Banach spaces and metric fixed point theory.
Geometric properties of composition operators belonging to Schatten classes.
Geometric properties related to the fixed point property in Banach spaces.
Geometric, spectral and asymptotic properties of averaged products of projections in Banach spaces
According to the von Neumann-Halperin and Lapidus theorems, in a Hilbert space the iterates of products or, respectively, of convex combinations of orthoprojections are strongly convergent. We extend these results to the iterates of convex combinations of products of some projections in a complex Banach space. The latter is assumed uniformly convex or uniformly smooth for the orthoprojections, or reflexive for more special projections, in particular, for the hermitian ones. In all cases the proof...
Géométrie du spectre dans une algèbre de Banach et domaine numérique
Dans une algèbre de Banach et dans deux cas particuliers, nous montrons la continuité du centre du plus petit disque contenant le spectre. Pour a ∈ , on donne une condition nécessaire et suffisante pour avoir où d(a) est la distance de a aux scalaires et le rayon du plus petit disque contenant K qui représente le spectre ou le domaine numérique algébrique de a. Dans un espace de Hilbert complexe, K peut représenter certains types de spectres ou de domaines numériques de a.
Geometry of numerical ranges in locally -convex *-algebras.
Geometry of oblique projections
Let A be a unital C*-algebra. Denote by P the space of selfadjoint projections of A. We study the relationship between P and the spaces of projections determined by the different involutions induced by positive invertible elements a ∈ A. The maps sending p to the unique with the same range as p and sending q to the unitary part of the polar decomposition of the symmetry 2q-1 are shown to be diffeomorphisms. We characterize the pairs of idempotents q,r ∈ A with ||q-r|| < 1 such that...
Geometry of some simple nonlinear differential operators
Geometry of the energy functional and the Fredholm alternative for the -Laplacian in higher dimensions.
Geometry of the spectral semidistance in Banach algebras
Let be a unital Banach algebra over , and suppose that the nonzero spectral values of and are discrete sets which cluster at , if anywhere. We develop a plane geometric formula for the spectral semidistance of and which depends on the two spectra, and the orthogonality relationships between the corresponding sets of Riesz projections associated with the nonzero spectral values. Extending a result of Brits and Raubenheimer, we further show that and are quasinilpotent equivalent if...
Ger-type and Hyers--Ulam stabilities for the first-order linear differential operators of entire functions.
Gestörte Verzweigung bei Potentialoperatoren.
Gewöhnliche Differentialgleichungen für Erzeugende gewisser Bergman-Operatoren.
Gleason measures and some inner products on the algebra of bounded operators on a Hilbert space
Global analysis for a two-dimensional elliptic eigenvalue problem with the exponential nonlinearity